A lady gives a dinner party for six guests. The number of ways in which they may be selected from among ten friends if two of the friends will not attend the party together is `112` b. `140` c. `164` d. none of these

Explanation

Number of guest `=6`

Total friends `=10`

Selection of 6 guest from ten friends `=10_{C_6}`

`=(10 !) /(6 ! cdot 4 !)` `=210` Selection of 2 friends always `=2_{C_2} times 8_{C_4}` `=1 times (8 ! )/(4 ! .4 !)` `=70`

Number of ways, to select 6 out of ten, when two will not attend the party together `=210-` `70=140`